For what condition does the quadratic equation ax^2 + bx + c = 0 have two equal real roots?
Answer and explanation
Correct answer: C. b^2 - 4ac = 0
- Step 1: The quadratic discriminant Delta = b^2 - 4ac determines root nature in the quadratic formula x = (-b +- sqrt(Delta)) / 2a. Step 2. When Delta = 0, the square root term vanishes, yielding a single repeated real root x = -b / 2a. Answer: b^2 - 4ac = 0. Why not the others: Delta > 0 gives two distinct real roots; Delta < 0 gives complex conjugate roots; b^2 + 4ac is not the discriminant.
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